Groups, Geometry, and Dynamics


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Volume 10, Issue 3, 2016, pp. 825–865
DOI: 10.4171/GGD/368

Published online: 2016-09-16

Integral foliated simplicial volume of hyperbolic 3-manifolds

Clara Löh[1] and Cristina Pagliantini[2]

(1) Universität Regensburg, Germany
(2) ETH Zürich, Switzerland

Integral foliated simplicial volume is a version of simplicial volume combining the rigidity of integral coefficients with the flexibility of measure spaces. In this article, using the language of measure equivalence of groups we prove a proportionality principle for integral foliated simplicial volume for aspherical manifolds and give refined upper bounds of integral foliated simplicial volume in terms of stable integral simplicial volume. This allows us to compute the integral foliated simplicial volume of hyperbolic 3-manifolds. This is complemented by the calculation of the integral foliated simplicial volume of Seifert 3-manifolds.

Keywords: Simplicial volume, integral foliated simplicial volume, hyperbolic 3-manifolds, measure equivalence

Löh Clara, Pagliantini Cristina: Integral foliated simplicial volume of hyperbolic 3-manifolds. Groups Geom. Dyn. 10 (2016), 825-865. doi: 10.4171/GGD/368